Nick is right. These are old-time terms that began when the whistles were actually sounded when boats met; one whistle for a port-to-port passing, two whistles for a starboard-to-starboard passing. With the advent of radio communication, the old terms stayed and are now used on the radio -- "I'll see you on the one".

Probably the hardest thing for some people to understand is the overtaking situation. Say I am faster than you are. I ask to pass you. I am the "burdened" vessel -- that is, the burden is on me to stay out of your way, since you are slower. You say "Come by me on two", which is MY two, since I am the burdened vessel. So, I come by you on two whistles, leaving you on my starboard side, just as if I met you on two, I would leave you on my starboard side.

Hope this answers your question!

This is, by the way, not just a towboat thing, but applies to ANY boat on the water! It applies from the smallest canoe to the largest ship, and everything in between.